Distorted Checker board
First of all, thanks for giving all the right info in your illustration. There's no object scaling, and you've shown us your texture space.
You're using the Object texture space, which is measured from the object's origin, along its own XYZ, before any object transforms,in Blender units. It's 3D. If you use a 3D texture, like the provided 'Checker' texture node, you will see no stretching: the pattern on the surface will be the one produced where the surface intersects a 3D grid of black and white cubes.
In the picture, on the other hand, you are using an Image texture, which is 2D. It only has X and Y coordinates, there's no Z to take into account, so, in Object space, it's projected straight down the object's Z, like a (UK) stick of rock. All points on the surface with the same Object XY get the same color from the image, where the surface intersects columns projected from black and white squares.
If you use a 2D image texture, you usually need a UV map to cut it up and plaster it over the surface in the desired way, and use the UV output of the Texture coordinate node.